MULTISOLITONS IN A 2-DIMENSIONAL SKYRME MODEL

The Skyrme model can be generalised to a situation where static fields are maps from one Riemannian manifold to another. Here we study a Sky rme model where physical space is two-dimensional euclidean space and the target space is the two-sphere with its standard metric. The model has topological soliton solutions which are exponentially localised. We describe a superposition procedure for solitons in our model and de rive an expression for the interaction potential of two solitons which only involves the solitons' asymptotic fields. If the solitons have t opological degree 1 or 2 there are simple formulae for their interacti on potentials which we use to prove the existence of solitons of highe r degree. We explicitly compute the fields and energy distributions fo r solitons of degrees between one and six and discuss their geometrica l shapes and binding energies.